Is a horrifyingly calm and methodical serial killer stalking residents of southwestern France? That’s the fear spreading through the region and the country after a gunman killed at least four people outside a Jewish school in Toulouse on Monday less than a week after four soldiers were slain in a similar manner during two separate attacks in the area. The probability of that scenario hardened further later Monday, when forensic experts reportedly confirmed the same gun was used in the school massacre and earlier strikes. So, as precautionary moves were made to increase security at Jewish organizations across France, investigators puzzled over whether the act was that of a lone madman or a possible terrorist conspiracy.

The latest bloodshed occurred shortly before 8 a.m. Monday, when a man on a black scooter opened fire outside the Ozar Hatorah school in a residential section of Toulouse. Three small children and one teacher were killed in the slaughter, during which, witnesses say, the assailant calmly pursued victims into the schoolyard. One of the two arms used was a .45-caliber pistol that experts later matched as the one that killed three French soldiers last week, according to reports. On March 11, one soldier was shot in Toulouse by a mask-wearing assassin on a scooter. Three days later, in the town of Montauban about 30 miles (50 km) north, three paratroopers were gunned down by a similar masked attacker on a scooter using the same .45-caliber weapon. Two of the three men in Montauban died — one after the assailant calmly walked over to finish the victim off with a shot to the head and then stared down horrified witnesses. In contrast to that attack, however, on Monday the assailant was apparently ready to claim as many victims at the Ozar Hatorah school as he could.

“He fired on everything in front of him — children or adults,” city prosecutor Michel Valet told reporters in Toulouse. “Children were chased inside the school.”

Ballistics tests confirming the same arm was used in all the attacks gave more force to other indications that the same attacker might have been behind all three. The gunman’s icy, determined manner of attack, masked identity and use of a high-powered scooter to get to and from the scene have many observers suspecting the same killer was involved. “It is too early to establish a sure link, but there are elements that justify asking very serious questions,” Valet said even before the results came back to identify the same gun in all three strikes.

Still, other aspects of the three attacks make drawing overarching conclusions harder. After the Montauban attack, it appeared likely the assailant was targeting members of the French military. Suspicions of a racial motive arose when it was learned that all three of the soldiers killed were ethnic Arabs and their injured peer is black. French terrorism investigators also started looking into whether the murders may have been part of a politically driven terrorism campaign targeting representatives of the French army — possibly in retaliation for France’s presence in Afghanistan. After Monday’s attack on the Jewish school, those terrorism specialists are widening that scope to examine whether one or several extremists may be aiming at members of what they consider various enemy groups in France.

The killings Monday deeply shook members of France’s Jewish community, which moved quickly to increase security outside Jewish schools and institutions around the country. Though France’s population of about 450,000 Jews — the largest in Europe — has suffered periodic spurts of racial abuse, physical aggression and vandalism that have coincided with surges of conflict between Israelis and Palestinians, the savagery of Monday’s attack in Toulouse was beyond any comparison. In addition, the cold, determined slaying of three children — ages 2, 6 and 8 — added another element of horror to what was already a shocking incident.

French President Nicolas Sarkozy initiated what became a collective halt in campaigning by candidates in France’s presidential election to pay tribute to victims in Toulouse. “It’s a day of national tragedy,” Sarkozy said. “The barbarity, the savagery, the cruelty cannot win. Hate cannot win. The nation is much stronger.”

And scared. Because as horrible as Monday’s school slaughter was, its potential ties to the two earlier attacks do little to flesh out the motives for the violence — or the identity of the killer. No evident similarities link soldiers, ethnic Arabs and Jewish students, which makes the assailant’s thinking harder to imagine or predict. Because of that — and despite the potential links connecting the attacks — authorities say they’re studying all theories.